Determine the number of solutions to this system of linear equations (0, 1, ∞): y=7x+8 −7x+y=−8 (1 point) This system of linear equations has how many solutions?
This system of linear equations has infinite solutions.
To determine the number of solutions to the system of linear equations, we need to analyze the coefficients of x and y.
The given system of equations is:
1) y = 7x + 8
2) -7x + y = -8
The first equation has a non-zero coefficient for x, which implies that it is not a horizontal line. Similarly, the second equation has a non-zero coefficient for x, indicating that it is also not a horizontal line.
Since both equations have non-zero coefficients for x and y, the lines represented by these equations are not parallel or coincident. Thus, they will intersect at a single point.
Therefore, the system of linear equations has only one solution.
To determine the number of solutions to the system of linear equations, we can analyze the slopes and intercepts of the two equations.
The first equation, y = 7x + 8, has a slope of 7. This means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 7. The intercept is 8, which indicates that the line crosses the y-axis at the point (0, 8).
The second equation, -7x + y = -8, can be rearranged to y = 7x - 8. This equation also has a slope of 7, meaning that it represents a line parallel to the first equation. The intercept is -8, indicating that the line crosses the y-axis at the point (0, -8).
Since the slopes of the two lines are equal, the lines are parallel and will never intersect. Therefore, there are no common points of intersection and no solutions to the system of linear equations.
In summary, the system of linear equations (y = 7x + 8) and (-7x + y = -8) has no solutions.